A trans cooler wonít help if there is suction side restriction or leak because itís the cavitation thatís causing the whine. Weíre assuming itís actual pump whine and not something else like an input bearing, pump bearing or such.
If it was my Jeep Iíd get an infrared thermometer and start taking temps at pan, cooler input/output lines and soup can coolant lines to rule out overheating. A cheap OBD interface and the Torque app will display trans temp.
Other things I would check is proper pan filter fitment, especially the filter oring and valve body interfaces and verify the fluid levels. Soup can heat exchanger can be removed, inspected and flushed, then reinstalled with a new coolant filter.
Ultimately if no progress is made you live with it or go down the rabbit hole and get an expert opinion from a reputable transmission shop and see where that leads and at what cost.